No comments about Pseudo Almost Periodic Functions in Banach Spaces.

No comments about Topological Vector Spaces: The Theory Without Convexity Conditions (Lecture Notes in Mathematics).

No comments about Stability Theory of Differential Equations.

No comments about Introduction to Operator Space Theory (London Mathematical Society Lecture Note Series).

No comments about Introduction to the Analysis of Metric Spaces (Australian Mathematical Society Lecture Series).

4 comments about Transition Mathematics.

1. For a student who is not very good at math this book was a great help. It clearly showed each formula and it also had a helpful Progress Self- Test at the end of each chapter. Leaves information at the students fingertips for easy retrival.



2. I have to use this book for school, its good until the 7th chapter, then it starts to get confusing. I now have to do Algebra- the second one in the series.



3. As a former K - 8 Mathematics Supervisor in high-flying school district, I can verify the validity of this Transition program in providing you the unique opportunity of actually being prepared for secondary mathematics of algebra, geometry, trigonometry, and precalculus, if you go that far. You should study this book beyond what your teacher does with it, because it is best applied as a two-year broad introductory mathematical program. If you do so, you will not be hit with a brick wall in trying to do the dreaded word problems in algebra and beyond. This book is relevant, the math is real, and it is backed with over twenty years of acutal research, instead of authors' best guesses as to what works. But it will take getting used to. If you're willing to make the effort, doors will open in your future.



4. I have not much to say. But for being from New Orleans and being rescued and all and trying to get used to a new school, it was tough. Then I failed math. Even worse. But this book so far is helping me catch up.

3 comments about Non-Linear Elastic Deformations.

1. I have a big problem with the Dover series to which this book belongs. The price may look good, but explanations are brief and visual representations of subjects treated are sparse. Don't buy this book.



2. This is a horribly written book. Instead of teaching non-linear elasticity to the reader, Ogden hides behind jargon and notation. Perhaps if you know finite elasticity very well, it would serve as a good reference.

   If you are interested in learning continuum mechanics, I recommend starting with Introduction to the Mechanics of a Continuous Medium, by L. E. Malvern. Then continue with Nonlinear Solid Mechanics: A Continuum Approach for Engineers, by G. A. Holzapfel.




3. It is easy to see why other reviewers do not like this book: it is very advanced. It is not for an undergraduate, and probably not for a graduate student unless she or he is already very familiar with elasticity and solid mechanics. It is not, at bottom, a text for learning the rudiments of the theory of elasticity: it is more on the level of a research monograph, and Malvern or Fung are better choices for many students. However, Ogden is probably the best work available (other than perhaps Truesdell, who can be an acquired taste) on the rigourous theory of non-linear elasticity. If you have an interest in the structure of constitutive relations, need a rigourous mathematical reference for finite element modeling, or are interested in exploring the assumptions and limitations of the linearised theory of elasticity, Ogden is not just the best place to start, but possibly the only place to go.

5 comments about Introduction To Fourier Optics.

1. This is the best book on Fourier Optics that I'm aware of. There is sufficient detail that you can follow the math, but also has well written text explaining concepts. The problems are sometimes trivial and sometime challenging, but they are very much an integral part of the book and doing them is necessary to get a full understanding of the material. There is a 3rd edition of the book with an additonal chapter, which is available at a much lower price, but Amazon does not seem to be carrying it yet. Hopefully they will soon. (...)



2. For the last month, I have been using this book for self study to aid me in my work with lasers. Originally, I was working from the 1st edition (borrowed from a co-worker), but decided to buy my own copy. I wound up buying the 3rd edition, a significantly expanded version of the original.
   
   Goodman's writing style is conversational and his treatment of the subject is thorough. I appreciate his inclusion of enough optics/E&M background within the text that I am not constantly having to go to my bookshelf to consult other references. Note, the 3rd edition has several helpful appendices not found in the 1st edition.
   
   There are also many instructive problems given throughout the text to help students solidify their understanding of the material.
   
   This is an excellent book for self study, and would certainly make a fine text for a senior undergrad course on the subject. I recommend it highly.
   
   Charlie.



3. Overall I like the book for it is clear, the mathematics is lucid and has all the essentials in a comprehensive way. I have found it quite useful for research. In addition, for the most parts it is quite accurate.
   
   Some criticisms though:
   Contains everything from a more mathematical point of view. By that i mean, problems are usually not very physically motivated and some of the conclusions drawn are not very physical. that is you are given at the end of a discussion only an integral. It would have been nice if there were more discussions on the physics of Fourier Optics, for example pictures of actual experimental results or clear diagrams that show for example how does the diffraction pattern for a given input looks like. So getting an intuitive grasp of the subject at a pictorial level, where you can 'see' the results is a bit challenging to get out of this book. also very expensive.



4. Only the best will do - and this is it.
   
   Mandatory reading for anyone involved in optics. Goodman's books are treasure troves.



5. I took a class in Fourier Optics and found this text to be indispensable. It explains everything very clearly and concisely, which is a minor miracle for a text at this level. I didn't have any particular background in optics, and was able to pick this up and understand every word.
   
   I do agree with the earlier poster that more 'physical' or graphical representations of concepts would have been useful as I tend to be a visual learner.

2 comments about Theory of Linear Operators in Hilbert Space.

1. This is a great intro to functional analysis. Having taken a graduate course on the subject, I used this as my text. The proofs are very readable and kept clear and simple. You'll see the subject develop before your eyes. One thing: when reading this book on infinite dimensional vector spaces, always try to draw a parallel with the finite dimensional version of the subject, linear algebra. You'll appreciate the book all the more. For every theorem relating to a bounded linear operator on Hilbert space, replace the operator by a matrix on Euclidean n-space.. you'll say "oh yeah! I remember that from linear algebra!"



2. The spectral theorem of David Hilbert, John von Neumann, and Marshall Stone gives a complete answer to the question of which operators admit a diogonal representation, up to unitary equivalence, and makes the question precise as well. The theorem states that these are the normal operators in Hilbert space. This includes the selfadjoint operators which represent observables in quantum physics, and the more interesting ones are unbounded. Remember the Heisenberg commutation relations do not admit bounded solutions. But there is a mathematical distinction between formally selfadjoint operators (also called symmetric operators) and the selfadjoint ones. It is only the latter to which the spectral theorem applies. The distinction between the two is understood from a pair of indicies (n,m), now called deficiency indices. In some applications they represent
   boundary conditions, and when n = m, and the boundary conditions are assigned, the symmetric operator in question has selfadjoint extensions. And we know from von Neumann what they are. A central question in the book concerns the issue of unequal indices. Then selfadjoint extensions do not exist, at least not unless the Hilbert space is enlarged. A central theme in the book is that in case of unequal indices, there is a larger Hilbert space which does in fact admit selfadjoint extensions. The co-authors, along with Naimark, are the authorities on this. Because of applications to PDE theory and to physics, there has been constant interest in the theme right up to the present. Even the current interest, and lively activity, in quantum measurement theory (in connection with quantum information theory) and entanglement brings back to to the fore this old issue around diagonalizing operators by passing to an "enlarged" (or dilated)Hilbert space, or looking for an orthonormal basis in the extended Hilbert space. So the theme of the book is still current.

5 comments about An Introduction to Hilbert Space.

1. An unusually readable book on Hilbert space. Very clean notation and very detailed proofs. There are also numerous diagrams. There are also answers to selected problems, but no detailed solutions. If you own one book on Hilbert space, or even functional analysis, this should be it. The author takes great pains to illustrate the ideas involved, not just pound out the theorems.



2. The first eleven chapters are an excellent introduction to functional analysis . Both Hilbert and Banach spaces are introduced carefully. Then there are two short chapters on orthogonal expansions and classical fourier series and then linear operators are studied. From the point of view of a person who is interested in applications to physics and engineering one can say that the book is well motivated mainly because is so compact and because of the many notes on applications. Chapters nine , ten and eleven on Green's functions and eigenfunctions expansions are extremely good. Chapters twelve and thirteen are poorly motivated from the point of view of applications.Finally chapters fourteen to sixteen try to exhibit the applications to complex analysis of operator theory and be helpfull to eletrical engineers.I think the book fails in this. So the ten first chapters of the book are excellent . The remaining less so



3. Young has done an admirable job at presenting some really beautiful and useful aspects of Hilbert spaces in a manner comprehendable for advanced undergraduates. After reading the book and reflecting on the experience, I'm somewhat amazed at the amount of nice ideas that were presented in such a compact text. The book cannot be compared with more rigorous and comprehensive texts such as Rudin, but you still get all the fundamentals of Hilbert space plus some wonderful applications.

   I must strongly disagree with the reader from Sao Paolo who says that chapters 12 and 13 are poorly motivated. These chapters are crucial for the final theorem of the book in chapter 16. Parrott's Theorem in chapter 12 is the key to the foundational Nehari's theorem of chapter 15. Chapter 13 explores Hardy spaces which are the setting place for the major theorem of Adamyan, Arov, and Krein in chapter 16. In fact, I found the movement of ideas from chapter 12 to chapter 16 to be marvelously compelling. These chapters have extreme importance for theoretically oriented control engineers.

   Only a modicum of real and complex analysis is necessary to understand the book. Knowledge of measure theory is not required.




4. This book is good to any control engineer who wants to know the background theory of optimization and robust control, but read read an analysis book first.



5. This book was the required text for a course on Hilbert Spaces at University of Edinburgh that I took back in 1998. This book is very readable, and does a great job of presenting the material. A great read if you plan to study Hilbert Spaces, Banach Spaces, or other topics in Functional Analysis at an introductory level.